Abstract :
Let A be a C∗-algebra generated by a nonself-adjoint idempotent e, and put K := sp(√e∗e) \ {0}. It is
known that K is a compact subset of [1,∞[ whose maximum element is greater than 1, and that, in general,
no more can be said about K. We prove that, if 1 does not belong to K, then A is ∗-isomorphic to the C∗-
algebra C(K,M2(C)) of all continuous functions from K to the C∗-algebra M2(C) (of all 2 × 2 complex
matrices), and that, if 1 belongs to K, then A is ∗-isomorphic to a distinguished proper C∗-subalgebra of
C(K,M2(C)). By replacing C∗-algebra with JB∗-algebra, sp(√e∗e) \{0} with the triple spectrum σ(e) of
e, and M2(C) with the three-dimensional spin factor C3, similar results are obtained.
© 2007 Elsevier Inc. All rights reserved
